# Publications

## Journals

Gaik Ambartsoumian and Venkateswaran P. Krishnan, "Inversion of a class of circular and elliptical Radon transforms", Contemporary Mathematics, American Mathematical Society, Proceedings of the international conference on Complex Analysis and Dynamical Systems VI, 2013 Preprint

Venkateswaran P. Krishnan and Eric Todd Quinto, "Microlocal analysis in tomography", in

*Handbook of Mathematical Methods in Imaging*, 2, In Press. PreprintSouvik Roy, Venkateswaran P. Krishnan, Praveen. C and A. S. Vasudevamurthy, "An efficient numerical algorithm for the inversion of an integral transform arising in ultrasound imaging", accepted in

*Journal of Mathematical Imaging and Vision*Preprint- Praveen C and C. Klingenberg, "A second order well-balanced finite volume scheme for Euler equations with gravity", SIAM J. Sci. Comp., vol. 37, Issue 3, pp. 382-402.
Anupam Pal Choudhury and Venkateswaran P. Krishnan, "Stability estimates for the inverse boundary value problem for the biharmonic operator with bounded potentials", To appear in

*Journal of Mathematical Analysis and Applications*. PreprintKevin Schaal, Andreas Bauer, Praveen Chandrashekar, Rüdiger Pakmor, Christian Klingenberg, Volker Springel, "Astrophysical hydrodynamics with a high-order discontinuous Galerkin scheme and adaptive mesh refinement", Monthly Notices of the Royal Astronomical Society - Main Journal, vol. 453, issue 4, Nov 2015, pp. 4278-4300. Preprint

Raluca Felea, Venkateswaran P. Krishnan, Clifford Nolan and Eric Todd Quinto, "Common midpoint versus common offset acquisition geometry in seismic imaging", to appear in

*Inverse Problems and Imaging*PreprintTuhin Ghosh and Venkateswaran P. Krishnan, "Determination of lower order perturbations of the polyharmonic operator from partial boundary data", to appear in Applicable Analysis Preprint

Ulrik S. Fjordholm and Deep Ray, "A sign preserving WENO reconstruction method", accepted in J. Sci. Comp. Preprint, Journal

- Deep Ray, Praveen Chandrashekar, Ulrik S. Fjordholm and Siddhartha Mishra, "Entropy stable schemes on two-dimensional unstructured grids for Euler equations", Communications in Computational Physics, vol. 19, issue 5, May 2016, pp. 1111-1140.
Praveen C and C. Klingenberg, "Entropy stable finite volume scheme for ideal compressible MHD on 2-D Cartesian meshes", SIAM J. Numerical Analysis., vol. 54, issue 2, pp. 1313-1340. Preprint

- Parish, E., Duraisamy, K., and Chandrashekar, P., "Generalized Riemann Problem-based Upwind Scheme for the Vorticity Transport Equations", Computers and Fluids, Vol. 132, pp. 10-18, June 2016.
- Juan Pablo Gallego-Valencia, Christian Klingenberg, Praveen Chandrashekar, "On limiting for higher order discontinuous Galerkin method for 2D Euler equations", Bulletin of the Brazilian Math Society, New Series, 47(1), pp. 335-354, March 2016.
Praveen. C, "Finite volume discretization of heat equation and compressible Navier-Stokes equations with weak Dirichlet boundary condition on triangular grids", International Journal of Advances in Engineering Sciences and Applied Mathematics, vol. 8, issue 3, pp. 174-193, Sep. 2016 Journal

- Debanjana Mitra, Mythily Ramaswamy and Jean-Pierre Raymond, "Largest space for the stabilizability of the linearized compressible Navier-Stokes system in one dimension", Math. Control Relat. Fields, 5 (2015), no. 2, 259-290.
- Shirshendu Chowdhury, Debayan Maity and Jean-Pierre Raymond, "Local Stabilization of Compressible Navier Stokes System around a null velocity in One Dimension", Jl. Differential Equns. 259 (2015) 371-407.
- Gaik Ambartsoumian and Souvik Roy, “Numerical inversion of a class of broken ray transforms with partial radial data in a disc”, IEEE Transactions on Computational Imaging: Vol 2, Issue 2, Pages: 166-173, doi: 10.1109/TCI.2016.2531581
- Souvik Roy, Mario Annunziato and Alfio Borzi, “A Fokker-Planck feedback control constrained approach for modelling crowd motion”, accepted for publication
Andreas Bauer, Kevin Schaal, Volker Springel, Praveen Chandrashekar, Rudiger Pakmor and Christian Klingenberg, "Simulating turbulence using the astrophysical discontinuous Galerkin code TENET", in Software for Exascale Computing - SPPEXA 2013-2015, Lecture Notes in Computational Science and Engineering, Springer, 2016. Arxiv, Journal

- Souvik Roy, Praveen Chandrashekar, A. S. Vasudeva Murthy, "A variational approach to estimate incompressible fluid flows", Proc. Indian Acad. Sci. (Math. Sci.), Vol. 127, No. 1, Feb 2017, pp. 175-201.
Praveen Chandrashekar and Markus Zenk, "Well-balanced nodal discontinuous Galerkin method for Euler equations with gravity", J. Sci. Comp., Vol. 71, Issue 3, pp. 1062-1093, June 2017. Arxiv, Journal

Asha Meena, Harish Kumar, Praveen Chandrashekar, "Positivity preserving high-order discontinuous Galerkin schemes for 10-moment Gaussian closure equations", Journal of Comp. Physics, Vol. 339, No. 15, pp. 370-395, June 2017. Journal

Debayan Maity, Takéo Takahashi, Marius Tucsnak, "Analysis of a system modelling the motion of a piston in a viscous gas", Journal of Mathematical Fluid Mechanics, 2016. Preprint

## Conferences/Workshops

Anupam Pal Choudhary, "Delta Waves and Explicit Formulae for Spherically Symmetric Solutions of the Multi-dimensional Zero-Pressure Gas Dynamics System", XV International Conference on Hyperbolic Problems: Theory, Numerics, Applications, IMPA, Brazil, July 2014 Slides

Imran Biswas, "Conservation laws driven by Levy white noise", XV International Conference on Hyperbolic Problems: Theory, Numerics, Applications, IMPA, Brazil, July 2014. Slides

Deep Ray, Praveen Chandrashekar, Ulrik S. Fjordholm and Siddhartha Mishra, "Entropy stable schemes for compressible flows on unstructured meshes", Poster presented at the Workshop on the Analysis and Numerical Approximation of PDEs, ETH Zurich, 8th-10th September, 2014 Poster

Deep Ray, Praveen Chandrashekar, Ulrik S. Fjordholm and Siddhartha Mishra, "Entropy stable schemes for compressible flows on unstructured meshes", Speaker at the the 5th International Conference on Scientific Computing and Partial Differential Equations, Hong Kong, 8th-12th December, 2014 Slides

Praveen. C, "Well-balanced schemes for Euler equations with gravity", Conference on Partial Differential Equations LNMIIT Jaipur, 10-11 December, 2014 Slides

- Venkateswaran P. Krishnan, Exact and approximate inversion methods in some imaging reconstruction problems, Recent and Emerging Trends in Computer and Computational Sciences (RETCOMP) 2015, PESIT South Campus, Bangalore, India, 08 January 2015.
- Venkateswaran P. Krishnan, Inversion of integral transforms arising in ultrasound imaging and related fields: Theory and Numerics, International Conference on Mathematical and Computational Biology (ICMCB), 2015, IIT Kanpur, India, 01 March, 2015
Praveen C, “Well-balanced discontinuous Galerkin method for the Euler equations with gravity”, Workshop on Higher Order Numerical Methods for Evolutionary PDEs: Applied Mathematics Meets Astrophysical Applications (15w5134), BIRS, Banff, Canada, 10-15 May 2015 Slides

- Venkateswaran P. Krishnan, Inversion of circular, elliptical and spherical Radon transforms: Theory and Numerics, Applied Inverse Problems Conference, Helsinki, Finland, 25-29 May, 2015.
- Rohit Kumar Mishra, Microlocal analysis of restricted ray transform in 3-dimensional Euclidean space, Contributed talk at Applied Inverse Problems Conference, Helsinki, Finland, 25-29 May 2015.
- Sombuddha Bhattacharyya, Recovering second order isotropic perturbation of a biharmonic operator from boundary data, Poster presentation at Applied Inverse Problems Conference, Helsinki, Finland, 25-29 May 2015.
Sreekar Vadlamani, "￼￼￼￼￼￼￼CLT for Lipschitz-Killing curvatures of excursion sets of Gaussian random fields", Conference on Extreme Values and Analysis, U. of Michigan, Ann Arbor, June 17, 2015 Slides

Mythily Ramaswamy, "Stabilization of one dimensional Compressible Navier-Stokes system”, Workshop on Fluid-Structure Interaction Problems, 29 June - 1 July, 2015, TIFR CAM, Bangalore. Slides

Praveen C, "Numerical implementation of feedback stabilization for Boussinesq model", Workshop on Fluid-Structure Interaction Problems, 29 June - 1 July, 2015, TIFR CAM, Bangalore. Slides

- Rohit Kumar Mishra, Exact inversion for restricted ray transform of symmetric m-tensor field in n-dimensional Euclidean space, Poster presentation in a topical workshop, Computational and Analytical Aspects of Image Reconstruction, ICERM, Brown University, Rhode Island, USA, 13-17 July 2015.
Deep Ray, "A sign preserving WENO reconstruction", International Conference on Industrial and Applied Mathematics, 10-14 Aug 2015, Beijing, China. Slides

- Venkateswaran P. Krishnan, Singular Fourier integral operators arising in some imaging problems, International Conference on Industrial and Applied Mathematics, 10-14 August 2015, Beijing, China.
Jayesh Badwaik, "Arbitrary Lagrangian Eulerian Discontinuous Galerkin Method for 1-D Euler Equations", Conference on Computational PDE, TIFR-CAM, Bangalore, 21-23 Dec, 2015. Slides

- Rohit Kumar Mishra, “Explicit and microlocal inversion of restricted ray transform in n-dimensional Euclidean space”, 8’th International Conference, Inverse Problems: Modeling and Simulation, May 23-28, 2016, Fethiye, Turkey
- Sombuddha Bhattacharyya, “Calderon type inverse problems on Riemannian manifolds”, 8’th International Conference, Inverse Problems: Modeling and Simulation, May 23-28, 2016, Fethiye, Turkey
- Manmohan Vashisth, “Inverse problems for the wave equation with underdetermined data”, 8’th International Conference, Inverse Problems: Modeling and Simulation, May 23-28, 2016, Fethiye, Turkey
Souvik Roy, “Inversion of spherical Radon transform in a spherical shell”, 8’th International Conference, Inverse Problems: Modeling and Simulation, May 23-28, 2016, Fethiye, Turkey Slides

- Praveen Chandrashekar, "Structure preserving schemes for conservation laws", International Conference on Advances in Scientific Computing, IIT Madras, 28-30 November, 2016. [Slides]
- Praveen Chandrashekar, "Discontinuous Galerkin method for rotating shallow water equation on the sphere", International Conference on Recent Advances in Theoretical and Computational PDE with Applications, Univ. Institute of Engineering and Technology, Panjab University, Chandigarh, 5-9 December, 2016. [Slides]
- Praveen Chandrashekar, "Discontinuous Galerkin and spectral element method for rotating shallow water equation on the sphere", Computational Science Symposium, Dept. of Computational and Data Sciences, IISc, Bangalore, 16-18 March, 2017. [Slides]
- Praveen Chandrashekar, "Discontinuous Galerkin and spectral element method for rotating shallow water equation on the sphere", PDES on the Sphere 2017, ENS, Paris, 3-7 April, 2017.

## Reports

Deep Ray, Praveen Chandrashekar, Ulrik S. Fjordholm and Siddhartha Mishra, "Entropy stable schemes on two-dimensional unstructured grids", Report number 2014-28, SAM, ETH Zurich, October 2014

## Master theses

- Sourav Mitra, "Feedback Stabilization of density dependent N-S equations”.
- Rohit Kumar Mishra, "Microlocal analysis of restricted Doppler transform in n-dimensional Euclidean space", July 2014
- Sombuddha Bhattacharyya, "Recovering second order Isotropic perturbation of a biharmonic operator from full boundary data", June 2014
- Manmohan Vashisth, "Inverse problems related to hyperbolic PDEs and hybrid imaging", July 2015

## PhD Theses

- Deep Ray, "Entropy stable finite difference and finite volume schemes for compressible flows", TIFR-CAM, May 2017.